Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
r = 170 m23 m/sac​ = ?

A 1600 kg car drives around a flat curve of radius 170 m at a constant 23 m/s. Find its centripetal acceleration ac.

m = 1600 kgv = 23 m/sr = 170 m
ac = m/s²
2.Easy
r = 0.7 mvmax​ = ?

A 0.8 kg stone is whirled in a horizontal circle of radius 0.7 m on a smooth, level table, held by a string that breaks at a tension of 200 N. Find the highest speed vmax the stone can have.

m = 0.8 kgr = 0.7 mTmax = 200 N
vmax = m/s
3.Medium
r = 85 mvmax​ = ?

A car takes a flat curve of radius 85 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 85 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
θ = ?to centre50 km/h

A road engineer wants cars to take a curve of radius 100 m at 50 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 100 mv = 50 km/hg = 9.81 m/s²
θ = °
5.Hard
r = 0.9 m12 m/svtop​ = ?

A 1.5 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 12 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.5 kgr = 0.9 mvbottom = 12 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 15°to centrevmax​ = ?

A curve of radius 140 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 140 mθ = 15°μs = 0.3g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. ac = 3.112 m/s²
  2. 2. vmax = 13.23 m/s
  3. 3. vmax = 24.16 m/s
  4. 4. θ = 11.12 °
  5. 5. Ttop = 166.4 N
  6. 6. vmax = 29.12 m/s

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